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\title{Automated modeling in \\qualitative reasoning}



\author{Hylke Buisman}


\institute[University of Amsterdam] % (optional, but mostly needed)
{
  BSc. Artificial Intelligence\\
  University of Amsterdam
}


\date{\today}

\renewcommand{\emph}[1]{\textcolor{blue}{#1}}





\begin{document}


% Een korte statement van waar we het over hebben
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\frame{\titlepage} 



\frame<article:1| beamer:0>[label=hidden1]
{
\tableofcontents[currentsection]
}


\section{Introduction}
\subsection{Intro stuff}


% Weinig zeggen, hoogstens kort noemen
\frame
{
\frametitle{Overview}

\begin{enumerate}
	\item Introduction
	\bigskip
	\item Approach
	\bigskip
	\item Algorithm
	\bigskip
	\item Results
	\bigskip
	\item Discussion \& conclusion
\end{enumerate}

}



\frame
{
\frametitle{Introduction}
\framesubtitle{Problem description}

\emph{Qualitative reasoning} (QR) uses conceptual models for knowledge representation and reasoning.
\emph{Successful applications} include:
\begin{itemize}
	\item Diagnostics in the automotive industry (Struss \& Price 2003)
	\item Knowledge representation in ecology (Salles et al. 2006)
\end{itemize}

\medskip
\medskip

\emph{Building models} for QR applications is \emph{difficult}:
\begin{itemize}
	\item Domain experts may not be familiar with modeling techniques
	\item Even when representation is known, modeling is a difficult task
\end{itemize}

\bigskip
\medskip

\emph{Automated modeling}
\begin{itemize}
	\item Automated modeling can facilitate the modeling process
\end{itemize}




}



\frame
{
\frametitle{Introduction}
\framesubtitle{Related work}

Prior work on \emph{model building}:
\begin{itemize}
	\item Mainly mathematical, and not very intuitive
	\item Cannot represent cause-effect relations
\end{itemize}

\bigskip

This thesis presents an algorithm for automatic modeling
which also \emph{captures cause-effect relations}.

\bigskip

Prior work in QR provides a \emph{vocabulary of primitives} for modeling and reasoning 
in this way:
\begin{itemize}
	\item Process-based qualitative reasoning (Forbus 1984)
	\item GARP3 (Bredeweg et al. 2006)
\end{itemize}

}

\section{Approach}
\subsection{Algorithm preliminaries}

\frame
{
\frametitle{Method}

\emph{Approach}
\begin{itemize}
	\item Algorithm designed by analyzing well established models
	\item Derive relations between the primitives and output behavior
\end{itemize}

\medskip

\emph{Algorithm}
\begin{itemize}
	\item \emph{input:} system behavior, system structure % from existing models: easy testing
	\item \emph{assumption:} all magnitudes/derivatives and quantities known
\end{itemize}

\medskip

\emph{Minimal covering}
\begin{itemize}
	\item finding a \emph{minimal} set of dependencies\\ that \emph{covers} (`explains') the input
\end{itemize}

\medskip

}


\frame
{
\frametitle{Models}

\begin{table}
	\centering
		\begin{tabular}{lp{2in}}
		\textbf{Model} & \textbf{Aspects}\\
		\hline
		\footnotesize Tree and shade growth & \scriptsize Small model, no conditions and interactions\\
			\hline
		\footnotesize Communicating vessels & \scriptsize Calculus element and (in)equalities\\
			\hline
	\footnotesize 	Deforestation & \scriptsize Many interconnected entities and quantities\\
			\hline
		\footnotesize Population dynamics & \scriptsize Interactions and conditions\\
			\hline
		\footnotesize Heating liquids & \scriptsize Interactions and conditions\\
			\hline
		\footnotesize Rstar & \scriptsize More types of conditions and many interactions\\
			\hline
		\footnotesize Ants Garden & \scriptsize idem\\
			
		\end{tabular}
\end{table}

}

\frame
{
\frametitle{Example}

\begin{columns}[C]
 \column{.4\textwidth}
 \begin{center}
 \includegraphics[scale=0.4]{treeSG.eps}\\ \medskip
 {\huge{+}}\\\medskip
  \includegraphics[scale=0.4]{treeVH.eps}
  \end{center}
 \column{.1\textwidth}
\textbf{{\Huge{$\Rightarrow$}}}
 \column[c]{.5\textwidth}
	\includegraphics[width=1.0\textwidth]{tree.eps}
\end{columns}


}


\section{Algorithm}
\subsection{Algorithm outline}

\frame
{
\frametitle{Algorithm: Naive dependencies}



\emph{Naive dependencies} are \emph{building blocks} for the rest of the algorithm:
\begin{itemize}
	\item Dependencies that do not involve interactions or conditions
	\item Result: consistent with the entire state-graph
\end{itemize}

\bigskip

The algorithm uses \emph{consistency rules}:
\begin{itemize}
	\item A dependency is selected if its consistency rule holds for the entire state-graph
\end{itemize}

\bigskip

The next steps will select the appropriate naive dependencies




}

\frame
{
\frametitle{Algorithm: Clusters}


 


\begin{columns}[C]
 \column{.6\textwidth}
 
 Naive dependencies are still very \emph{unstructured}
\begin{itemize}
	\item \emph{Clusters} are used to bring structure
	\item Quantities are structured in groups with \emph{similar behavior}
\end{itemize}

\bigskip

Two quantities are in a cluster when:
\begin{itemize}
	\item They have (inverse) corresponding behavior
	\item They belong to the same entity
\end{itemize}
 
 
 \column[c]{.4\textwidth}
\includegraphics[width=0.80\textwidth]{clusters.eps}
	
\end{columns}

}





\frame
{
\frametitle{Algorithm: Causal paths}




\begin{columns}[C]
 \column{.4\textwidth}
 
 
 \includegraphics[width=0.80\textwidth]{causal_paths.eps}
 \column[c]{.6\textwidth}

	 To describe the system's causality, \emph{causal paths} are identified
\begin{itemize}
	\item Within clusters all possible paths are enumerated
	\item Cluster paths are combined into partial models
\end{itemize}

\bigskip

Inconsistent partial models are \emph{filtered}
\begin{itemize}
	\item Quantities under the same entity type should have the same order
\end{itemize}

\end{columns}


}

\frame
{
\frametitle{Algorithm: Cluster actuation}

Clusters have no use by themselves: \emph{they need to be connected}\\
\emph{Two possibilities} can be distinguished:\\
\begin{itemize}
	\item \textit{Equilibrium seeking mechanism}\\
		Actuation through \emph{flows}
	\item \textit{External actuators}\\
	Actuation through an external force
\end{itemize}
\medskip
Actuation candidates are based on naive dependencies



}


\frame
{
\frametitle{Algorithm: Cluster linking}

Some clusters remain isolated:
\begin{itemize}
	\item They are linked with propagations
\end{itemize}
\bigskip\bigskip
Finding the linking order is similar to finding causal orderings in clusters

}



\frame
{
\frametitle{Algorithm: Setting initial magnitudes (1)}
Before simulation is possible, \emph{initial values need to be set}\\
\emph{Some may already be set}:
\begin{itemize}
	\item Value assignments in scenario
	\item Via correspondence with known quantities
\end{itemize}

\bigskip


\begin{center}
 \includegraphics[width=0.60\textwidth]{../images/IV_correspondence.eps}
\end{center}
}


\frame
{
\frametitle{Algorithm: Setting initial magnitudes (2)}
\emph{Other unknowns} are set with one of the following:
\begin{itemize}
	\item \emph{Initializing calculi}\\
	Analyze initial states to derive (in)equalities
		
	\item \emph{Conditionless value assignments}\\
	Check whether there one value is consistent with entire state-graph	
	\item \emph{Conditional value assignments }\\
	Place conditions on `neighboring' quantities
	\item \emph{Values as conditions in model fragments}\\
	Analyze initial values in state-graph to identify ambiguity
\end{itemize}



}


\frame
{
\frametitle{Algorithm: Dependency interactions}

Advanced models often require \emph{interactions} to be handled.

\medskip

	\begin{center}
		\includegraphics[scale=0.5]{../images/infl_interact.eps}
	\end{center}


\bigskip

All possible interactions are checked using consistency rules

}

\section{Results \& discussion}
\subsection{Final}

\frame
{
\frametitle{Model results - What?}

\begin{table}
	\centering
		
		\begin{tabular}{p{1.5in}p{2in}}
		\textbf{Model} & \textbf{Aspects}\\
		\hline
	
		\footnotesize Tree and shade growth 	& \scriptsize Modeled correctly\\
	
			\hline
		\footnotesize Communicating vessels & \scriptsize Causal dependencies found correctly, equality statement not found\\
			\hline
		\footnotesize Deforestation & \scriptsize Modeled correctly, causal ordering differs (correctly)\\
			\hline
		\footnotesize Population dynamics & \scriptsize Dependencies identified, initial values not all determined\\
			\hline
		\footnotesize Heating liquids, Rstar {\& Ants Garden} & \scriptsize Incorrect output
		\end{tabular}
\end{table}



}

\frame
{
\frametitle{Model results - Why?}

\begin{table}
	\centering
		
		\begin{tabular}{p{1.5in}p{2in}}
		\textbf{Model} & \textbf{Aspects}\\
		\hline
	
		\footnotesize Tree and shade growth 	& \scriptsize Small and simple, no complex constructs\\
			\hline
		\footnotesize Communicating vessels & \scriptsize Limited magnitude initialization implementation\\
			\hline
		\footnotesize Deforestation & \scriptsize Causal ordering according to rules, produces arguable better results\\
			\hline
		\footnotesize Population dynamics & \scriptsize  Limited magnitude initialization\\
			\hline
		\footnotesize Heating liquids, Rstar {\& Ants Garden} & \scriptsize Complex models with unhandled dependencies
		\end{tabular}
\end{table}


}


\frame
{
\frametitle{Discussion and conclusion}

\emph{Conclusion:} By studying increasingly complex models, a \emph{\textit{successful algorithm}} for automated QR modeling is designed. \emph{\textit{Concrete suggestions }}for improvement have been made.

\bigskip

\emph{Discussion:} Initial value setting, interactions and conditions should be further investigated in order to handle fully complex models.

\bigskip

\emph{Future work:}
\begin{itemize}
	\item Add interaction with the user
	\item Apply iterated interaction with the reasoning engine
	\item Split generated model based on fragment reusability
\end{itemize}

\bigskip 




}

\end{document}